MK · Practice test

Mathematics Knowledge Practice Test 2

Mathematics Knowledge Practice Test 2 leaves out the algebraic expressions and linear equations lessons, shifting weight toward number sense, inequalities and geometry. Number properties and divisibility, inequalities, and quadrilaterals and polygons stand out, with signed numbers, exponents and roots, systems, functions and sequences, angles, triangles, circles, area and volume, and coordinate graphs rounding it out.

15 questions
31 minutes
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Mathematics Knowledge

15 questions · 31 min on the real test

Question 1 · MK · easy

Rewrite $4^{- 2}$ without a negative exponent. Which value is it equal to?

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Answer: B

Correct answer: 1/16. A negative exponent means the reciprocal with a positive exponent:

4^{- 2} = \frac{1}{4 ^{2}} = \frac{1}{16}

A: A negative exponent makes a fraction, not a negative number.
B (correct): Take the reciprocal: 1 over $4^{2}$ , which is 1/16.
C: This uses 4 × 2 = 8 in the denominator instead of $4^{2} = 16$ .
D: This multiplies 4 by −2 and treats the result as negative.

Question 2 · MK · easy

A rectangular rug is 9 feet long and 6 feet wide. How many square feet of floor does it cover?

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Answer: B

Correct answer: 54 square feet. Use

A = lw

A = 9 \times 6 = 54 square feet

A: This adds the length and width instead of multiplying them.
B (correct): Area of a rectangle is length times width: 9 times 6 is 54.
C: This doubles the area, as if a perimeter-style factor of 2 belonged in the formula.
D: This is the perimeter, 2 times (9 + 6), which measures the edge, not the covered floor.

Question 3 · MK · easy

What is the value of $- (- 12) - 5$ ?

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Answer: C

Correct answer: 7. The two negative signs cancel, so

-(-12) = 12 then 12 - 5 = 7

A: This treats −(−12) as −12, missing that the double negative is positive.
B: This gives the right size with the wrong sign; 12 − 5 is positive.
C (correct): −(−12) is 12, and 12 − 5 = 7.
D: This adds 5 instead of subtracting it after rewriting −(−12) as 12.

Question 4 · MK · easy

What is the next term of the sequence 2, 6, 18, 54, ...?

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Answer: B

Correct answer: 162. Divide consecutive terms:

6 / 2 = 3 and 18 / 6 = 3

so the common ratio is 3. The next term is 54 times 3 = 162.

A: This adds 18, the previous term, rather than multiplying by the common ratio.
B (correct): Each term is 3 times the one before (r = 54 / 18 = 3), so the next term is 54 times 3 = 162.
C: This adds 36, the last gap, treating a geometric pattern as if the gaps were steady.
D: This doubles 54, using a ratio of 2 instead of the actual ratio of 3.

Question 5 · MK · medium

A garden plot is made of a 15 m by 8 m rectangle joined along its 15 m side to a trapezoid. The trapezoid's parallel sides are 15 m and 9 m, and its height is 4 m. What is the total area of the plot?

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Answer: B

Correct answer: 168 square meters. Rectangle: 15 times 8 = 120 square meters. Trapezoid: half of (15 + 9) times 4 = 12 times 4 = 48 square meters. Total:

120 + 48 = 168 square meters

A: This forgets the one half in the trapezoid formula, giving 96 instead of 48.
B (correct): Add the rectangle, 120, to the trapezoid, one half times 24 times 4 = 48.
C: This treats the trapezoid as a 15 by 4 rectangle, using only the longer base.
D: This treats the trapezoid as a 9 by 4 rectangle, using only the shorter base.

Question 6 · MK · medium

A circle has a radius of 8 inches. How long is the arc cut off by a central angle of 135 degrees?

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Answer: A

Correct answer: 6π inches. The angle fraction is

135/360 = 3/8

The full circumference is 2π(8) = 16π inches, so the arc is 3/8 of 16π = 6π inches.

A (correct): The fraction 3/8 of the 16π-inch circumference is 6π inches.
B: This takes 3/8 of the area, 64π; arc length uses the circumference.
C: This is the full circumference; only 3/8 of the circle is cut off.
D: This takes 3/8 of 8π, using πr instead of the full circumference 2πr.

Question 7 · MK · medium

An exterior angle of a triangle measures 117°. One of its two remote interior angles measures 49°. What is the measure of the other remote interior angle?

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Answer: D

Correct answer: 68°. An exterior angle equals the sum of the two remote interior angles, so

117 = 49 + x and x = 117 - 49 = 68

°.

A: 63° is the interior angle adjacent to the exterior angle (180 - 117), not a remote interior angle.
B: This adds the two given angles; the exterior angle is already the sum of the remote angles.
C: This subtracts both given angles from 180°, treating 117° as if it were an interior angle.
D (correct): The exterior angle equals the sum of the remote interior angles: 117 - 49 = 68°.

Question 8 · MK · medium

A coach has 42 red cones and 70 blue cones. She wants to set them out in identical groups, each with the same number of red cones and the same number of blue cones, with no cones left over. What is the greatest number of groups she can make?

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Answer: B

Correct answer: 14 groups. Identical groups with nothing left over call for the GCF.

42 = 2 \times 3 \times 7 and 70 = 2 \times 5 \times 7

so the GCF is

2 \times 7 = 14

Each group gets

42 \div 14 = 3

red and

70 \div 14 = 5

blue cones.

A: 7 divides both numbers, but it is not the greatest common factor.
B (correct): The GCF of 42 and 70 is 14, so she can make 14 groups of 3 red and 5 blue cones.
C: 8 is the number of cones in each group (3 red + 5 blue), not the number of groups.
D: 210 is the LCM; it cannot be the number of groups because there are only 112 cones.

Question 9 · MK · medium

Each interior angle of a regular polygon measures 140 degrees. How many sides does the polygon have?

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Answer: B

Correct answer: 9 sides. Each exterior angle is

180 - 140 = 40 degrees

The exterior angles total 360 degrees, so

n = 360 / 40 = 9

sides.

A: This subtracts 2 from the correct 9, mixing in the n - 2 from the angle-sum formula.
B (correct): The exterior angle is 40 degrees, and 360 / 40 = 9.
C: This stops at the exterior angle, 40 degrees, and reports it as the number of sides.
D: This halves the exterior angle to 20 degrees before dividing 360 by it.

Question 10 · MK · medium

If n is any integer, which of the following expressions must be even?

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Answer: B

Correct answer: n(n + 3). Adding an odd number (3) switches parity, so exactly one of n and n + 3 is even. A product with at least one even factor is even. For example, n = 5 gives

5 \times 8 = 40

A: n and n + 2 have the same parity; if n is odd, both factors are odd and the product is odd.
B (correct): n and n + 3 always have opposite parity, so one factor is even and the product is even.
C: 2n is even, so adding 1 always makes the result odd.
D: Adding 4 keeps the parity of n, so the result is odd whenever n is odd.

Question 11 · MK · medium

Which inequality describes every value of x that satisfies

7 - 3 x > 22

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Answer: C

Correct answer:

x < -5

Subtract 7 from both sides:

-3x > 15

Divide both sides by −3 and reverse the sign:

x < -5

Check

x = -6 7 + 18 = 25

which is greater than 22.

A: This divides by −3 but forgets to reverse the inequality sign.
B: This reverses the sign but drops the negative when dividing 15 by −3.
C (correct): Subtracting 7 gives −3x > 15; dividing by −3 reverses the sign, giving x < −5.
D: This adds 7 to 22 instead of subtracting it before dividing by −3.

Question 12 · MK · hard

Which inequality has no solution?

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Answer: B

Correct answer:

4(x - 2) > 4x + 1

Distribute:

4 x - 8 > 4 x + 1

Subtract 4x from both sides:

- 8 > 1

That statement is false no matter what x is, so the inequality has no solution.

A: The x terms cancel and leave 8 > 1, which is always true, so every real number is a solution.
B (correct): Distributing gives 4x − 8 > 4x + 1; the x terms cancel, leaving −8 > 1, which is always false.
C: The x terms do not cancel; solving gives 2x > 9, so x > 4.5 is the solution set.
D: The x terms do not cancel; solving gives −x > 7, so x < −7 is the solution set.

Question 13 · MK · hard

A transversal crosses two parallel lines. At the upper intersection the angles are numbered 1 (top left), 2 (top right), 3 (bottom left) and 4 (bottom right); angles 5, 6, 7 and 8 sit in the same positions at the lower intersection. Angle 1 measures $(4 x + 10)^{\circ}$ and angle 7 measures $(2 x + 20)^{\circ}$ . What is the measure of angle 6?

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Answer: A

Correct answer: 70°. Same-side exterior angles are supplementary:

(4x + 10) + (2x + 20) = 180

so 6x = 150 and x = 25. Angle

7 = 2(25) + 20 = 70

°, and angle 6 is vertical to angle 7, so angle 6 = 70°.

A (correct): Angles 1 and 7 are same-side exterior, so 6x + 30 = 180 and x = 25; angle 7 is 70°, and angle 6 is vertical to it.
B: This is the value of x, not the measure of angle 6.
C: This is angle 1; angle 6 is not equal to angle 1 but supplementary to it.
D: This sets angles 1 and 7 equal, getting x = 5, but same-side exterior angles are supplementary.

Question 14 · MK · hard

A line passes through (-3, 10) and (6, -2). At what point does it cross the x-axis?

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Answer: C

Correct answer: (4.5, 0). Slope:

m = (-2 - 10)/(6 - (-3)) = -12/9 = -4/3

Substitute (-3, 10):

10 = 4 + b

so b = 6 and

y = (-4/3)

x + 6.

Set y = 0: (4/3)x = 6, so x = 6 times

3/4 = 4.5

The x-intercept is (4.5, 0).

A: This is the y-intercept, where the line crosses the y-axis instead.
B: The sign was lost when solving; with a negative slope and positive y-intercept, the line crosses the x-axis to the right of the origin.
C (correct): The line is y = (-4/3)x + 6; setting y = 0 gives (4/3)x = 6, so x = 4.5.
D: This multiplies 6 by 4/3 instead of dividing 6 by 4/3.

Question 15 · MK · hard

3x + 2y = 18 and x - 2y = -2

what is the value of $x^{2} - y$ ?

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Answer: C

Correct answer: 13. Add the equations: 4x = 16, so x = 4. Then

4 - 2y = -2

gives y = 3. Finally,

x^{2} - y = 16 - 3 = 13

A: This is x + y; the question asks for the square of x minus y.
B: This drops the negative sign on −2 during back-substitution, giving y = 1.
C (correct): Adding gives x = 4, then y = 3, so 16 − 3 = 13.
D: This is x − y; x must be squared first.

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About this test

You get 15 original questions and 31 minutes, the same format as the other MK forms. Four questions are easy, seven medium and four hard. No question here is repeated in another practice test, so retaking a different form later gives you an honest comparison. MK counts toward the AFQT, which makes steady practice on it worth the time.

Set a quiet half hour aside and answer without a calculator, as on test day. After submitting, read the explanation for each wrong or uncertain answer and revisit the matching lesson. If you want algebra practice specifically, pair this form with one that includes linear equations. Your result is practice accuracy only and does not stand in for an ASVAB score.

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